### Abstract

The study is about impact of a short elastic rod(or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to predict stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. In the process of predicting the stress and velocity of wave propagation using viscoelastic discontinuity, the Z-effective which is the effective ratio of acoustic impedance plays important role. It can be shown that effective ratio of acoustic impedance can help us to determine whether the slug and the rod move together or part company after the impact. After modeling the impact and solve the governing system of partial differential equations in the Laplace transform domain. We invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the predictable stresses and velocities using viscoelastic discontinuity analysis.

Original language | English |
---|---|

Title of host publication | International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013 |

Pages | 146-151 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 11 Nov 2013 |

Event | International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Kuala Lumpur, Malaysia Duration: 05 Feb 2013 → 07 Feb 2013 |

### Publication series

Name | AIP Conference Proceedings |
---|---|

Volume | 1557 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Other

Other | International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 |
---|---|

Country | Malaysia |

City | Kuala Lumpur |

Period | 05/02/13 → 07/02/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Ecology, Evolution, Behavior and Systematics
- Ecology
- Plant Science
- Physics and Astronomy(all)
- Nature and Landscape Conservation

### Cite this

*International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013*(pp. 146-151). (AIP Conference Proceedings; Vol. 1557). https://doi.org/10.1063/1.4823893

}

*International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013.*AIP Conference Proceedings, vol. 1557, pp. 146-151, International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013, Kuala Lumpur, Malaysia, 05/02/13. https://doi.org/10.1063/1.4823893

**The effective ratio of acoustic impedance in predicting stress and velocity of wave propagation in viscoelastic material (standard linear solid model).** / Haji Musa, Abu Bakar.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - The effective ratio of acoustic impedance in predicting stress and velocity of wave propagation in viscoelastic material (standard linear solid model)

AU - Haji Musa, Abu Bakar

PY - 2013/11/11

Y1 - 2013/11/11

N2 - The study is about impact of a short elastic rod(or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to predict stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. In the process of predicting the stress and velocity of wave propagation using viscoelastic discontinuity, the Z-effective which is the effective ratio of acoustic impedance plays important role. It can be shown that effective ratio of acoustic impedance can help us to determine whether the slug and the rod move together or part company after the impact. After modeling the impact and solve the governing system of partial differential equations in the Laplace transform domain. We invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the predictable stresses and velocities using viscoelastic discontinuity analysis.

AB - The study is about impact of a short elastic rod(or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to predict stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. In the process of predicting the stress and velocity of wave propagation using viscoelastic discontinuity, the Z-effective which is the effective ratio of acoustic impedance plays important role. It can be shown that effective ratio of acoustic impedance can help us to determine whether the slug and the rod move together or part company after the impact. After modeling the impact and solve the governing system of partial differential equations in the Laplace transform domain. We invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the predictable stresses and velocities using viscoelastic discontinuity analysis.

UR - http://www.scopus.com/inward/record.url?scp=84887066188&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887066188&partnerID=8YFLogxK

U2 - 10.1063/1.4823893

DO - 10.1063/1.4823893

M3 - Conference contribution

SN - 9780735411838

T3 - AIP Conference Proceedings

SP - 146

EP - 151

BT - International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013

ER -